Quasiconformal Homogeneity after Gehring and Palka

In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of R ¯ n . Their definition was later extended to hyperbolic manifolds. In this paper we survey the theory of quasiconformally homogeneous subsets o...

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Bibliographic Details
Published in:Computational methods and function theory 2014-10, Vol.14 (2-3), p.417-430
Main Authors: Bonfert-Taylor, Petra, Canary, Richard, Taylor, Edward C.
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
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Summary:In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of R ¯ n . Their definition was later extended to hyperbolic manifolds. In this paper we survey the theory of quasiconformally homogeneous subsets of R ¯ n and uniformly quasiconformally homogeneous hyperbolic manifolds. We furthermore include a discussion of open problems in the theory.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-014-0057-z